Flashcard on Proportions and Literal Equations

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you solve for a variable in a proportion?

Back

To solve for a variable in a proportion, cross-multiply and then isolate the variable.

Front

What is a literal equation?

Back

A literal equation is an equation that involves two or more variables.

Front

How do you isolate a variable in a literal equation?

Back

To isolate a variable in a literal equation, use algebraic operations to get the variable on one side of the equation.

Front

What is the formula for solving for n in the equation \( \frac{m}{n} = \frac{p}{q} \)?

Back

The formula is \( n = \frac{mq}{p} \).

Front

If 20 Fuji apples cost $12, how do you set up a proportion to find how many apples you can buy for $3?

Back

Set up the proportion as \( \frac{20}{12} = \frac{x}{3} \) and solve for x.

Front

What is the first step in solving the equation a - b + c = 9 for a?

Back

The first step is to add b and subtract c from both sides to isolate a.

Front

What is the solution for m in the equation m - n = 5?

Back

The solution is m = n + 5.

Front

What does it mean to cross-multiply in a proportion?

Back

Cross-multiplying means multiplying the numerator of one ratio by the denominator of the other ratio.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal.